Microscopic Three-cluster Model Research Articles

Theoretical analysis of the reactions induced by interaction of Li6 with H3 and He3 nuclei

We determine cross sections and astrophysical S factors of the reactions generated in collisions between Li6 and H3 and between Li6 and He3. A microscopic three-cluster model is employed to study the dynamics of reactions occurring in the mirror nuclei Be9 and B9. In a previous study [], this model was successfully applied to investigate the resonance structure of Be9 and B9, as well as reactions induced by the interaction of deuterons with Li7 and Be7. A fairly good agreement between theoretical results and available experimental data was achieved. To the best of our knowledge, appropriate experimental data for the astrophysical S factors of the reactions generated by the interaction of Li6 with H3 and with He3 are currently unavailable. Thus, our results can serve as a guideline for future experimental efforts. Published by the American Physical Society 2024

Spectroscopic amplitudes in microscopic three-cluster systems

I investigate three-body spectroscopic amplitudes in a microscopic three-cluster model. The total wave functions are described in the resonating group method (RGM) formalism based on cluster wave functions and on relative functions defined in the hyperspherical method. Core excitations are included. I develop a method aimed to determine three-body spectroscopic amplitudes and spectroscopic factors. This technique also provides three-body wave functions where the antisymmetrization is treated approximately. In this way, the various channels are orthogonal to each other and can be used without the antisymmetrization operator. This method is well known in two-cluster systems, and is based on the eigenvalues and the eigenvectors of the antisymmetrization operator. I illustrate the formalism with the $^{6}\mathrm{He}$, $^{11}\mathrm{Li}$, and $^{14}\mathrm{Be}$ nuclei where $^{9}\mathrm{Li}$ and $^{12}\mathrm{Be}$ excited states are taken into account.

Microscopic Model of Radiative Capture Reactions with Cluster Polarizability. Application to 7Be and 7Li

We apply the microscopic three-cluster model developed by the authors to study effects of cluster polarization on the capture reactions 3He(α, γ)7Be, 3He(α, γ) 7Li, 6Li(p, γ)7Be and 6Li(n, γ)7Li. These reactions are of great importance for the astrophysical applications. Thus main attention is paid to the cross section (or the astrophysical S factor) of the reactions at low energies. We also study thoroughly the correlations between the astrophysical S factor of the reactions at zero energy and various quantities associated with the ground state of a compound nucleus.

Microscopic three-cluster study of light exotic nuclei

I develop a microscopic three-cluster model for exotic light nuclei. I use the hyperspherical formalism, associated with the Generator Coordinate Method. This model is well adapted to halo nuclei, since the long-range part of the radial wave functions is accurately reproduced. The core wave functions are described in the shell model, including excited states. This technique provides large bases, expressed in terms of projected Slater determinants. Matrix elements involve seven-dimension integrals, and therefore require long calculation times. I apply the model to 11Li, 14Be, 15B, and 17N described by two neutrons surrounding a 9Li, 12Be, 13B and 15N core, respectively. The 17Ne (as 15O+p+p) and 15Ne (as 13O+p+p) mirror nuclei are briefly discussed. I present the spectra and some spectroscopic properties, such as r.m.s. radii or E2 transition probabilities. I also analyze the importance of core excitations.

Microscopic Description of $${^{8}{\hbox {Li}}{+}}$$ 8 Li + Nucleus and of $${^{8}{\hbox {B}}{+}}$$ 8 B + Nucleus Scattering

We apply a microscopic version of the Continuum Discretized Coupled Channel (CDCC) method, referred to as MCDCC, to $$^{8}{\hbox {Li}}$$ and $$^{8}{\hbox {B}}$$ scattering on different targets. The $$^{8}{\hbox {Li}}$$ and $$^{8}{\hbox {B}}$$ nuclei are described in a microscopic three-cluster model ( $$\alpha +t+n$$ and $$\alpha + {^{3}}\mathrm{He}+p$$ ), using the hyperspherical coordinates. We first present spectroscopic properties of these nuclei. Then, we determine $$^{8}{\hbox {Li}}+$$ nucleus and $$^{8}{\hbox {B}}+$$ nucleus potentials by using proton $$+$$ target and neutron $$+$$ target interactions. We compute various elastic-scattering cross sections and confirm that breakup effects are important, in particular at low energies. In general, we find a fair agreement with experiment, except for $${^{8}}\mathrm{B}\,+^{58}\text{ Ni }$$ where we suggest that the data might be overestimated.

Formation and decay of resonance states in Be9 and B9 nuclei: Microscopic three-cluster model investigations

We study nature of the low-lying resonance states in mirror nuclei $^{9}$Be and $^{9}$B. Investigations are performed within a three-cluster model. The model makes use of the hyperspherical harmonics, which provides convenient description of three-cluster continuum. The dominant three-cluster configurations $\alpha+\alpha+n$ and $\alpha+\alpha+p$ in $^{9}$Be and $^{9}$B, respectively, are taken into account. Dominant decay channels for all resonance states in $^{9}$Be and $^{9}$B are explored. Much attention is paid to the controversial $1/2^{+}$ resonance states in both nuclei. We study effects of the Coulomb interaction on energy and width of three-cluster resonances in the mirror nuclei $^{9}$Be and $^{9}$B. We also search for the Hoyle-analogue state which is a key step for alternative way of $^{9}$Be and $^{9}$B syntheses in a triple collision of clusters in a stellar environment.

Microscopic three-cluster model of 10Be

We investigate spectrum of bound and resonance states in 10Be, and scattering of alpha-particles on 6He. For this aim we make use of a three-cluster microscopic model. This model incorporates Gaussian and oscillator basis functions and reduces three-cluster Schrödinger equation to a two-body like many-channel problem with the two-cluster subsystem being in a bound or a pseudo-bound state. Much attention is given to the effects of cluster polarization on spectrum of bound and resonance states in 10Be, and on elastic and inelastic He6+α scattering.

Formation and decay of resonance state in 9Be and 9B nuclei. Microscopic three-cluster model investigations

We study nature of the low-lying resonance states in mirror nuclei 9Be and 9B. Investigations are performed within a three-cluster model. The model make uses of the hyperspherical harmonics, which provide convenient description of three-cluster continuum. Much attention is paid to the controversial 1/2+ resonance states in both nuclei. We study effects of Coulomb interaction on energy and width of three-cluster resonances in the mirror nuclei 9Be and 9B. We look for the Hoyle-analogue states which allows for alternative way of 9Be and 9B synthesis in a triple collision of clusters.

Three-cluster model of radiative capture reactions in seven-nucleon systems. Effects of cluster polarization

We apply the microscopic three-cluster model, developed by the authors recently, to study the effects of cluster polarization on the capture reactions 3He(α, γ)7Be, 3H(α, γ)7Li, 6Li(p, γ)7Be, and 6Li(n, γ)7Li. These reactions are of great importance for astrophysical applications. Thus, the main attention is paid to the cross sections (or the astrophysical S factor) of the reactions in the low-energy region. Correlations between the astrophysical S factor of the reactions at zero energy and different quantities associated with the ground state of a compound nucleus are studied in detail.

MICROSCOPIC STUDY OF THREE-BODY SCATTERING STATES

We investigate continuum states of the α+n+n and α+p+p systems using a microscopic three-cluster model in the hyperspherical formalism. The A-nucleon wave functions are defined in the generator coordinate method (GCM). The R-matrix method is used to connect the wave functions to their exact asymptotic behaviors and to derive the collision matrix. We present the three-body phase shifts of the 0+ and 1- continuum of the α+n+n and α+p+p systems.

A microscopic three-cluster model with nuclear polarization applied to the resonances of 7Be and the reaction 6Li( p, 3He) 4He

A microscopic model for three-cluster configurations in light nuclei is presented. It uses an expansion in terms of Faddeev components for which the dynamic equations are derived. The model is designed to investigate binary channel processes in a compound system. Gaussian and oscillator bases are used to expand the wave function and to represent appropriate boundary conditions. We study the effect of cluster polarization on ground and resonance states of 7Be, and on the astrophysical S-factor of the reaction 6Li( p, 3He) 4He.

Decay of 5H in a microscopic three-cluster model

The Pauli-allowed states of a three-cluster model are shown to be orthonormal polynomials of a discrete variable, which become the Kravchuk polynomials as the number of oscillator quanta increases. Such asymptotic behavior corresponds to the subsequent decay of the 5H into the 4H and a neutron.

Comparison of local, semi-microscopic, and microscopic three-cluster models

Two different three-body models are compared with a fully antisymmetrized microscopic three-cluster model. The local model makes use of local effective interactions involving forbidden states among the three particles. In the semi-microscopic model, nonlocal two-body interactions are derived within the resonating-group method from the same nucleon-nucleon effective forces as in the microscopic model. In both cases, calculations are performed in hyperspherical coordinates with the Lagrange-mesh method. The role of forbidden states and their elimination are discussed. The models are applied to an $\ensuremath{\alpha}\ensuremath{\alpha}n$ description of $^{9}\mathrm{Be}$ and an $\ensuremath{\alpha}\mathit{nn}$ description of $^{6}\mathrm{He}$. The local model results are affected by almost forbidden states and may be unrealistic for $^{9}\mathrm{Be}$. A comparison of the microscopic and semi-microscopic models shows that the effect of exchanges involving the three clusters is weak. An overbinding of $^{9}\mathrm{Be}$ cannot be avoided with nucleon-nucleon forces reproducing $\ensuremath{\alpha}n$ and $\ensuremath{\alpha}\ensuremath{\alpha}$ scattering properties. On the contrary, $^{6}\mathrm{He}$ is underbound under the same conditions. This can probably be attributed to a lack of three-nucleon forces.

A microscopic three-cluster model in the hyperspherical formalism

The hyperspherical formalism is applied in the framework of the microscopic generator-coordinate method. Three-cluster systems are described with a single generator coordinate, the hyperradius. This model is a natural extension of previous microscopic theories, and can be applied to bound states and resonances in a range of nuclei exhibiting a cluster structure. As an illustrative example, the model is applied to 6He and 6Li. Density distributions and electric dipole transition strengths are calculated, including B( E2;0 +→2 +) in 6He. The results are consistent with a neutron halo structure for the ground state of 6He, and with a proton–neutron halo structure of its isobaric analog state in 6Li. No 1 − “soft dipole” resonance is found in 6He.

Resonance states of5Hand5Bein a microscopic three-cluster model

Resonance states of ${}^{5}\mathrm{H}$ and ${}^{5}\mathrm{Be}$ have been studied using microscopic $t+n+n$ and $h+p+p$ three-cluster models, respectively. The resonance positions are localized by the three-body complex scaling method. An effective nucleon-nucleon interaction, which reproduces the $\ensuremath{\alpha}+N$ low energy phase shifts and the energies of the ${0}^{+}$ ground and ${2}^{+}$ first excited states of ${}^{6}\mathrm{He}$ with the three-cluster model, is used to calculate resonance states of ${}^{5}\mathrm{H}$ and ${}^{5}\mathrm{Be}.$ This model can reasonably reproduce the experimental $t+n$ and $h+p$ phase shifts at low energies. It gives a ${1/2}^{+}$ broad resonance as the ground state in ${}^{5}\mathrm{H}$ and ${}^{5}\mathrm{Be}$ and in addition it gives two excited resonance states of ${3/2}^{+}$ and ${5/2}^{+}.$ The resonance parameters of the ${1/2}^{+}$ state of ${}^{5}\mathrm{H}$ in the present model are close to those deduced from their recent experimental data by Korsheninnikov et al. The same effective nucleon-nucleon interaction is used for a tentative investigation in order to explore the possibility of a tetra-neutron ${(}^{4}n)$ resonance by means of the $n+n+n+n$ four-body complex scaling method on a restricted set of model configurations. Our model does not give any evidence for a tetraneutron resonance.

Low-energy photodisintegration of9Bewith the molecular orbit model

We use a microscopic three-cluster model with the $\alpha+\alpha+n$ configuration to analyze with astrophysical interests the photodisintegration cross section of $^9$Be. The valence neutron in $^9$Be is treated in the molecular orbit model (MO), including continuum states by the box discretization method. It is shown that good agreement is achieved with the recently measured B(E1) transition probability from the ground state to the first 1/2$^+$ state when the box size is enlarged, resulting in reasonable reproduction of the experimental data for the photodisintegration cross section. The Coulomb dissociation of $^9$Be is also discussed.

Microscopic study of α clustering in 12C, 24Mg and 48Cr

A microscopic three-cluster model is used to investigate the 12C, 24Mg and 48Cr nuclei, described by α+α+α, 16O+α+α and 40Ca+α+α configurations, respectively. For each system, a fairly good agreement with experiment is obtained. We essentially focus on the 48Cr nucleus for which a band structure is suggested. In addition to the well-known ground-state band, we predict the existence of additional bands.

Microscopic three-cluster study of the low-energy 9 Be photodisintegration

The 9Be and 9B nuclei are investigated in a microscopic three-cluster model involving α + α + n (or α + α + p) configurations. The 8Be (0 + , 2 + ) + n and 5He (3/2 - , 1/2 - ) + α (or mirror) channels are included by taking account of the unstable nature of 8Be and 5He. Spectroscopic properties of 9Be and 9B are analyzed. We show that the 5He + α configurations cannot be neglected to derive accurate results. The 9Be(γ,αα)n photodisintegration cross-section is shown to be mainly determined by 8Be + n channels at low energies, but 5He + α channels become important beyond E γ≈ 4 MeV.

Soft dipole mode in the 11Li nucleus within the asymptotic-potential approximation

A soft dipole mode in the 11Li nucleus treated within the microscopic three-cluster model is studied in the asymptotic-potential approximation. The model faithfully reproduces the energy and the root-means-quare radius of the ground state and the behavior of the effective photodisintegration cross section at low energies above the threshold for 11Li breakup, suggesting the existence of two resonance states in this region.

Effects of 8B size on the low-energy 7Be(p,γ) 8B cross section

We calculate several “size-like” 8B observables within the microscopic three-cluster model and study their potential constraints on the zero-energy astrophysical S 17(0) factor of the 7Be(p,γ) 8B reaction. We find within our three-cluster model that a simultaneous reproduction of the experimental data for the 8B radius and quadrupole moment and of the 8B 8Li Coulomb displacement energy implies S 17(0) = (23–25) eV b.